Performs Cholesky factorization on a symmetric or Hermitian positive definite matrix. Wire data to the A input to determine the polymorphic instance to use or manually select the instance.


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The following equations show the factorization of A for real cases and complex cases, respectively:

A = RTR A = RHR

where R is an upper triangular matrix, and all the diagonal elements of R are positive.

The Cholesky factorization exists only if the matrix A is positive definite and either symmetric or Hermitian. If A is not symmetric or Hermitian, this VI uses only the upper triangular portion of A. If A is not positive definite, this VI returns an error.

You can use Cholesky factorization to solve linear equations. For example, to solve the linear equation Ax = b, where A is a positive symmetric matrix and A = RTR, you can derive the following equations: Rx = h, and h = R–Tb. Then you can use the triangular property of matrix R to solve the equations.

Examples

Refer to the following example files included with LabVIEW.

  • labview\examples\Mathematics\Linear Algebra\Linear Algebra Calculator.vi